The corrosion and anti-corrosion current of a ship modulated by the shaft can be equivalent to a time-harmonic current. Based on Maxwell's equations and boundary conditions of electromagnetic field, the Helmholtz equation of magnetic vector potential and the magnetic field expressions of the time-harmonic current in air are deduced. Then, the fast Hankel transform filtering algorithm is applied to solve the equations which contain Bessel integral. The theoretic calculation indicates that the magnetic induction intensity and its attenuation rate decrease along with the increase of distance. The three components of magnetic field have different distribution. At last, it is verified that the shaft-rate magnetic field can be observed by the experiments of carbon electrodes and ship model carried in a sea pool.
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